"Looser tolerances" is an internet myth. As defined in blueprints and engineering specs, a tolerance is the allowable variation from the specific dimension, for ex. +/- .030. That means the part can vary from .970 to 1.030 from the specified 1.000" dimension.
What the AR industry enjoys is getting that dimension within .003" and doing it across the board with any of four dozen makers. CNC metalworking is that good now.
CLEARANCES are designed spaces between parts to allow movement and accept some of the variation in production tolerances, expansion from heat, contraction from cold, and buildup of detritus in a working mechanism. The AR does not have specifically tighter clearances for it's design. That misconception goes back to the false assumption it jams when exposed to excessive gas residue. That doesn't happen.
What does happen is a casual shooter noticing the piston bolts all rattle around on rails to guide them - the AR carrier is contained in a tube, almost completely enclosed. The BCG rattles around plenty on it's own, it's just quieted down by the constant spring load against it. A piston bolt doesn't always have that loading on it's carrier.
The untrained anecdotal perspective is that the AR bolt carrier must be a tighter fit, and proven to be so by the myth of jamming up from gas residue - which isn't a problem, either. It's been demonstrated by Mike Panone an AR will go 2,400 rounds fired completely dry, about ten basic loads of ammo. No soldier goes a week of combat without maintaining his weapon daily. Another carbine, Filthy 14, has gone 50,000 rounds + with nothing more than a wipedown and more lube. It doesn't stop up and jam from tight tolerances or gas residue.
"Loose tolerances" isn't happening - that would be a .998" bolt carrier trying to fit a .997" AR upper. That doesn't happen, and the clearances are plenty big enough. Most stoppages are bad magazines/ammo, or a lack of preventative maintenance in replacing worn out parts.